Analysis of stress and strain in a rotating disk mounted on a rigid shaft

The plane state of stress in an elastic-perfectly plastic isotropic rotating annular disk mounted on a rigid shaft is studied. The analysis of stresses, strains and displacements within the disk of constant thickness and density is based on the Mises yield criterion and its associated flow rule. It is observed that the plastic deformation is localized in the vicinity of the inner radius of the disk, and the disk of a sufficiently large outer radius never becomes fully plastic. The semi-analytical method of stress-strain analysis developed is illustrated by some numerical examples.

Elastsete-platsete telgsümmeetriliste plaatide analüüs ja optimeerimine

Väitekirja elektrooniline versioon ei sisalda publikatsioone.Insenerimehaanikast on teada, et konstruktsioonielementide (talade, plaatide, koorikute) projekteerimisel on materjali kokkuhoiuks mõistlik arvestada lisaks elastsetele deformatsioonidele ka plastseid. Elastse deformatsiooni korral taastub keha esialgne kuju pärast koormuse eemaldamist, plastse deformatsiooni korral mitte. Antud töös vaadeldakse nn sandwich-tüüpi ümar- ja rõngasplaate, millele mõjub telgsümmeetriline ristkoormus. Ümarplaat on ringsilindriline keha, mille kõrgus on teiste mõõtmetega võrreldes väike. Sandwich-tüüpi plaadiks nimetatakse ideaalset kahekihilist plaati, mille kandva kihi paksus h on kihtidevahelise kaugusega H võrreldes väike. Kogu plaat on elastne, kui talle rakendatakse väikseid koormusi. Koormuse suurendamisel tekib plaadis üks või mitu plastset piirkonda. Doktoritöös uuritakse erinevate kinnitusviisidega tükati konstantse paksusega elastseid-plastseid ümar- ja rõngasplaate tükati lineaarsete voolavustingimuste korral. Elastse-plastse konstantse paksusega välisservast vabalt toetatud rõngasplaadi paindeülesaande lahendamiseks leitakse erinevate koormuste korral analüütiliselt ja numbriliselt plaadi läbipainded ning radiaal- ja tangentsiaalsuunalised paindemomendid. Selgub, et tükati konstantse paksusega elastse-plastse seest jäigalt kinnitatud ja välisservast täiesti vaba astmelise rõngasplaadi pingeseisundi saab jagada kolme erinevasse staadiumisse. Leitakse läbipainde ja paindemomentide avaldised vastavalt elastse, elastse-plastse ja täiesti plastse plaadi pingeseisundi korral. Numbriliselt lahendatakse ühe astmega elastsete homogeensest ja anisotroopsest materjalist ümarplaatide optimeerimisülesanded, kus etteantud plaadi ruumala korral arvutatakse optimaalsed kandvate kihtide paksused ning astme asukoht nii, et plaadi keskpunkti läbipaine oleks minimaalne. Samuti leitakse ringikujuliste lisatugede optimaalsed asukohad vabalt toetatud elastse ümarplaadi puhul nii, et plaadi läbipaine oleks minimaalne.When modelling the structural behaviour of the structural elements (e.g. beams, plates, shells), it is necessary to account for both the plastic and elastic deformations. In the case of elastic deformation the body recovers its initial shape after removing the loading, in the case of plastic deformation it does not recover. In this work, the so-called sandwich-type circular and annular plates under axisymmetric transverse loading are studied. A circular plate is a cylinder with a much smaller height compared to its radius. A sandwich-type plate is an ideal two-layered plate where the height of the carrying layers h is much smaller than the thickness of the core material H. Under small loads, the entire plate is elastic. Increasing of the load may cause the appearance of one or several plastic areas in the plate. In this thesis, the circular and annular plates with the piecewise constant thickness and different support types are investigated using piecewise linear yield conditions. The bending problem for the elastic plastic annular plate, simply supported at the outer edge, is solved by finding the deflections, the radial and circumferential bending moments for different loadings. It appears that the stress strain state of the elastic plastic annular plate with the piecewise constant thickness, clamped at the inner edge and absolutely free at the outer edge, can be divided into three stages. The expressions of the deflections and the bending moments are found in the cases of elastic, elastic plastic and entirely plastic stress strain states, respectively. The optimization problems regarding to the stepped circular plates made of homogeneous and anisotropic materials are solved numerically. For the fixed plate volume, the optimal values for the heights of the carrying layers and the location for the step are calculated while requiring minimal deflection at the centre of the plate. Also, the optimal locations for additional circular supports corresponding to the minimum of the mean deflection are found in the case of the elastic simply supported plate

Robust estimation of limit loads of plates using secant rigidity

A robust method for the estimation of limit loads of structures has been adopted for plate structures. It involves the use of modified secant rigidity. The method makes use of repeated linear elastic analyses to predict limit behavior. The results from an initial elastic analysis are used to obtain the principal moments. A suitable yield criterion (such as Tresca or Von Mises) in terms of generalized forces is used. A set of equivalent moments is then computed for the plate. This is used to modify the secant rigidity of the plate. The modified structure is re-analyzed iteratively until convergence is reached. The moment distribution from the convergent analysis shows the collapse mechanism for the plate. The average of the equivalent moments along the collapse (or yield) lines of the plate is scaled to the plastic moment capacity of the section to obtain the limit load factor. The method has several advantages in comparison to other traditional methods. -- This method has been implemented on ANSYS software using APDL routines. Problems solved include: simply supported and fixed square and circular plates with uniform and concentrated loads, plates with irregular boundary conditions and shapes as well as continuous plates with checkerboard loading. The results from the above analyses match analytical results very closely, thus demonstrating the usefulness of the method used

Key issues in computational geomechanics

As stated in the introduction, the three main topics covered in this report are actual research fields. Different analyses and new developments related with these fields have been presented in the previous chapters. In the following, after a brief summary of the contributions, some directions for future research are outlined. Detailed presentations of the conclusions of each contribution are included in the corresponding sections and subsections. The most relevant contributions of this report are the following: 1. With respect to the treatment of large boundary displacements: > Quasistatic and dynamic analyses of the vane test for soft materials using a fluid–based ALE formulation and different non-newtonian constitutive laws. > The development of a solid–based ALE formulation for finite strain hyperelastic–plastic models, with applications to isochoric and non-isochoric cases. 2. Referent to the solution of nonlinear systems of equations in solid mechanics: > The use of simple and robust numerical differentiation schemes for the computation of tangent operators, including examples with several non-trivial elastoplastic constitutive laws. > The development of consistent tangent operators for substepping time–integration rules, with the application to an adaptive time–integration scheme. 3. In the field of constitutive modelling of granular materials: > The efficient numerical modelling of different problems involving elastoplastic models, including work hardening–softening models for small–strain problems and density– dependent hyperelastic–plastic models in a large–strain context. > Robust and accurate simulations of several powder compaction processes, with detailed analysis of spatial density distributions and verification of the mass conservation principle

Stress analysis of operating gas pipeline installed by horizontal directional drilling and pullback force prediction during installation

With the development of the natural gas industry, the demand for pipeline construction has also increased. In the context of advocating green construction, horizontal directional drilling (HDD), as one of the most widely utilized trenchless methods for pipeline installation, has received extensive attention in industry and academia in recent years. The safety of natural gas pipeline is very important in the process of construction and operation. It is necessary to conduct in-depth study on the safety of the pipeline installed by HDD method. In this dissertation, motivated by the following considerations, two aspects of HDD are studied. First, through the literature review, one issue that has not received much attention so far is the presence of stress problem during the operation condition. Thus, two chapters (Chapters 3 and 4) in this dissertation are related to the pipe stress problem during the operation. Regarding this problem, two cases are considered according to the fluidity of drilling fluid. The more dangerous situation is determined by comparing the pipeline stress in the two working conditions. The stress of pipeline installed by HDD method and open-cut method is compared, and it indicates that the stress of pipeline installed by HDD method is lower. Moreover, through the analysis of influence factors and stress sensitivity, the influence degree of different parameters on pipeline stress is obtained. Secondly, literature review indicates that the accurate prediction of pullback force in HDD construction is of great significance to construction safety and construction success. However, the accuracy of current analytical methods is not high. In the context of machine learning and big data, three new hybrid data-driven models are proposed in this dissertation (Chapter 5) for near real-time pullback force prediction, including radial basis function neural network with complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN-RBFNN), and support vector machine using whale optimization algorithm with CEEMDAN (CEEMDAN-WOA-SVM), and a hybrid model combines random forest (RF) and CEEMDAN. Three novel models have been verified in two projects across the Yangtze River in China. It is found that the prediction accuracy is dramatically improved compared with the original analytical models (or empirical models). In addition, through the feasibility analysis, the great potential of machine learning model in near real-time prediction is proved. At the end of this dissertation, in addition to summarizing the main conclusions obtained, three future research directions are also pointed out: (1) stress analysis of pipelines installed by HDD in more complex situations; (2) stress analysis of pipeline during HDD construction; (3) database establishment in HDD engineering

Stress Analysis of Operating Gas Pipeline Installed by Horizontal Directional Drilling and Pullback Force Prediction During Installation

With the development of the natural gas industry, the demand for pipeline construction has also increased. In the context of advocating green construction, horizontal directional drilling (HDD), as one of the most widely utilized trenchless methods for pipeline installation, has received extensive attention in industry and academia in recent years. The safety of natural gas pipeline is very important in the process of construction and operation. It is necessary to conduct in-depth study on the safety of the pipeline installed by HDD method. In this dissertation, motivated by the following considerations, two aspects of HDD installation are studied. First, through the literature review, one issue that has not received much attention so far is the presence of stress problem during the operation condition. Thus, two chapters (Chapters 3 and 4) in this dissertation are related to the pipe stress analysis during the operation. Regarding this problem, two cases are considered according to the fluidity of drilling fluid. The more dangerous situation is determined by comparing the pipeline stress in the two working conditions. The stress of pipeline installed by HDD method and open-cut method is also compared, and it indicates that the stress of pipeline installed by HDD method is lower. Moreover, through the analysis of influence factors and stress sensitivity, the influence degree of different parameters on pipeline stress is obtained. Secondly, literature review indicates that the accurate prediction of pullback force in HDD construction is of great significance to construction safety and construction success. However, the accuracy of current analytical methods is not high. In the context of machine learning and big data, three new hybrid data-driven models are proposed in this dissertation (Chapter 5) for near real-time pullback force prediction, including radial basis function neural network with complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN-RBFNN), support vector machine using whale optimization algorithm with CEEMDAN (CEEMDAN-WOA-SVM), and a hybrid model combines random forest (RF) and CEEMDAN. Three novel models have been verified in two projects in China. It is found that the prediction accuracy is dramatically improved compared with the original analytical models (or empirical models). In addition, through the feasibility analysis, the great potential of machine learning model in near real-time prediction is proved. At the end of this dissertation, in addition to summarizing the primary conclusions, three future research directions are also pointed out: (1) stress analysis of pipelines installed by HDD in more complex situations; (2) stress analysis of pipeline during HDD construction; (3) database establishment in HDD engineering

Manifested flatness predictions in thin strip cold rolling

International audienceThe paper deals with flatness defects prediction in thin plates which appear during rolling. Their origin is the roll stack thermo-elastic deformation. The combination of the elastic deflection, the thermal crown and the roll grinding crown results in a non-parallel bite. If the transverse roll profile is not an affinity of the incoming strip profile, differential elongation results and induces high stresses in the outgoing strip. The latter combine with the imposed strip tension force, resulting in a net post-bite stress field which may be sufficiently compressive locally to promote buckling. A variety of non-developable shapes may result, generally occurring as waviness, and classified as flatness defects (center waves, wavy edges, quarterbuckles...). The purpose of the present paper is to present a coupled approach, following [1]: a simple buckling criterion is introduced in the FEM model of strip and roll deformation, LAM3/TEC3 [2]. The post-bite stress field is in much better agreement with experiments if this treatment is used, as will be demonstrated

Nonlinear Constitutive Relations for High Temperature Application, 1984

Nonlinear constitutive relations for high temperature applications were discussed. The state of the art in nonlinear constitutive modeling of high temperature materials was reviewed and the need for future research and development efforts in this area was identified. Considerable research efforts are urgently needed in the development of nonlinear constitutive relations for high temperature applications prompted by recent advances in high temperature materials technology and new demands on material and component performance. Topics discussed include: constitutive modeling, numerical methods, material testing, and structural applications

Running-in and residual stress: finite element contact analysis of as measured rough surfaces and comparison with experiment

The principal aim of this thesis was to investigate the contact and deformation of rough surfaces such as those found on the teeth of gears. Freshly manufactured surfaces undergo a process known as “running-in”, in which the surface geometry is altered as a result of contact under load. Plastic deformation can occur which induces significant residual stresses, and it has been suggested that these may have implications for the subsequent fatigue life of the surfaces. In this thesis, finite element analysis (FEA) has been used to perform full elastic-plastic contact analysis based on profiles from gear teeth which are used in micropitting tests in order to determine the detailed nature of deformation and the magnitude and distribution of the residual stresses. FEA was performed using Abaqus, and the techniques were first developed using known contact problems of smooth elastic bodies. Plastic behaviour was subsequently introduced, guided by previous studies in the literature. Profiles from real surfaces were then used to study the behaviour of typical gear surfaces under load. Experiments were carried out in which the rough surfaces of crowned steel discs were loaded together, with relocated profiles taken before and after loading. The aim was to provide experimental verification of the residual deformations predicted by FEA. Good agreement was found between the analysis and experiments carried out at different loads. Regions of surface and subsurface residual tensile stress were predicted to occur in proximity to heavily loaded asperity contacts. Greater plastic deformation resulted in increased magnitudes of residual stress. Significant residual tensile stresses were predicted in regions where crack initiation has been shown to occur in practice at depths typical of micropitting failures in gears. It is concluded that residual effects of initial plastic deformation taking place during running-in can be a significant factor in micropitting failures in gears